Munich Personal RePEc Archive
Multiple Reserve Requirements, Exchange Rates, Sudden Stops and
Equilibrium Dynamics in a Small Open Economy
Wang, Wen-Yao and Hernandez-Verme, Paula
Texas AM University at Galveston, Texas AM University at College Station
5 March 2009
Online at https://mpra.ub.uni-muenchen.de/13802/
MPRA Paper No. 13802, posted 06 Mar 2009 07:36 UTC
1
Multiple Reserve Requirements, Exchange Rates, Sudden Stops and Equilibrium Dynamics in a Small Open Economy
March 3, 2009
Wen-Yao Wang
Texas A&M University at Galveston
Paula Hernandez-Verme
Texas A&M University at College Station
Abstract
We model a typical Asian-crisis-economy using dynamic general equilibrium techniques. Meaningful exchange rates obtain from nontrivial demands for fiat currencies. Sudden stops/bank-panics are possible, and key for evaluating the relative merits of alternative exchange rate regimes in promoting stability.
Strategic complementarities contribute to the severe indeterminacy of the continuum of equilibria; there is a strong association between the scope for existence and indeterminacy of equilibria, the properties along dynamic paths and the underlying policy regime. Binding multiple reserve requirements reduce the scope for financial fragility and panic equilibria; backing the money supply acts as a stabilizer only in fixed regimes.
JEL Classification: E31, E44, F41
Keywords: Sudden stops; Exchange rate regimes; Multiple reserve requirements.
1. Introduction
We study the interaction between monetary policies and alternative exchange rate regimes to ascertain the probability of a crisis, building from the characteristics of the Asian-crisis countries in 1997. Our broader goal is to reinforce and fill in the link between the overexpansion of the financial system, banking crises, and exchange rate regimes/monetary policy that we find lacking in the literature. With this in mind, we build a Dynamic Stochastic General Equilibrium Model (DSGE) --from micro-foundations-- replicating a small, open economy (SOE) with a nontrivial banking system, such as one of the 1997 East Asian countries. Two words of caution to the reader: First, this paper does not aim, from a historical point of view, to show the success of a particular monetary policy in place either in defending the national currency or in managing contagion at the time of the crisis. Our goal, instead, takes the form of a ―what if:‖ what if a typical Asian-crisis-country were
We owe special thanks to David Bessler, Li Gan and Dennis Jansen for helpful comments and suggestions to previous versions of this paper. We thank Teri Tenalio for her technical assistance. We would also like to thank the participants of the 2007 Midwest Macroeconomic Meetings for helpful suggestions, as well as the participants of the 2007 Southwestern Association Meetings.
Corresponding author. E-mail: wenyaowang@tamu.edu
Corresponding author. E-mail: phernandez@econmail.tamu.edu
2
to implement a policy of multiple reserve requirements with backing of the domestic money supply, and how would it work under alternative exchange rate arrangements? Thus, we look forward and aim to suggest policy options that may help these countries maintain stability in case a similar crisis was to hit again. Second, at this time, we do not consider economic activity explicitly other than in the financial sector.
Our model captures all five stylized facts of the East Asian countries at the time of the crisis. It is general knowledge that Indonesia, South Korea, and Thailand were the countries most affected by the East Asian 1997/98 crisis, followed by Malaysia, Laos and the Philippines. There are five stylized facts shared by these countries at the time of the crisis that we want to emphasize. 1) Increased risky-lending behavior by banks led to a boom in private borrowing financed by non-performing loans1. 2) The lack of sound financial structure worsened with the ill-oriented process of financial and capital liberalization2. 3) Banks’ financial assets constituted the majority of their total assets –instead, for instance, of financing in capital markets. 4) Borrowing from foreign banks was a significant portion of domestic banks’ loans. 5) The majority of these countries had intermediate pegs in place. According to the standard chronology of the crisis, the floating of the baht in July 1997 in Thailand triggered the crisis. A subsequent change in expectations led to the depreciation of most currencies in the region, bank runs, rapid withdrawals of foreign capital --a sudden stop—and a dramatic economic downturn followed. Unlike previous crises originated from fiscal imbalances and/or trade deficits, the Asian crises shed light on the increased risky behavior and the overexpansion of the banking system.
To build the framework that we just described, we used three building blocks that took us closer to our goal systematically. In the first block, we model explicitly the behavior of individuals and obtain the micro- foundations for our general equilibrium model. In the second block, we introduce alternative exchange rate regimes with their associated monetary policy rules. It is a well-established fact that for economies open to international capital flows, the choice of exchange rate regime is central to explain the vulnerability and fragility of financial markets, as well as domestic price stability and long-run viability. Tables 1.A and 1.B summarize the exchange rate arrangements in the Asian countries. During most of the 1980s and the first part of the 1990s, Indonesia, Korea, Thailand and Malaysia had managed floating arrangements --an intermediate peg--, while Philippines had free floating. However, there were some important differences after the 1997 crises: Philippines continued with free floating, Indonesia, Korea and Thailand moved from intermediate pegs to free floating as well, but Malaysia had a very hard peg in place. These facts make our comparison of the relative merits of the two sets of policy rules relevant in the presence of binding multiple reserve requirements.
The third building block may allow one to infer behavior from a particular set of circumstances: we may be able to separate and identify causes and
1 One may also think of this fact in the context of the subprime mortgage crisis that started in the second-part of 2007 in the U.S.
2 See Lindgren et al (1999) and Kishi and Okuda (2001).
3
consequences by studying separately and jointly the main stylized facts of sudden stops and bank-runs in similar economies3.
We consider two potential causes of crises: a crisis comes to our model either in the form of a sudden stop of foreign credit (intrinsic uncertainty) or in the form of a panic among national depositors (extrinsic uncertainty.) We put most of our effort on the distinguishing characteristic of the former but do not neglect the fact that a self-fulfilling panic and run may implicitly aggravate a crisis.
We believe that we improve on C-V in at least three dimensions. First, C-V attached intrinsic value to currencies they intended to be fiat4. We instead take multiple fiat currencies –domestic and foreign—a bit more seriously, and introduce non-trivial demands for them. In particular, banks must hold a fraction of their deposits as unremunerated currency reserves: a fraction to be held in the form of domestic currency and another fraction in the form of foreign currency. Then, fiat money instead enters our model by the regulation that governs the multiple reserve requirements in this economy5, the implications being that: 1) there is a meaningful nominal exchange rate in our model, and 2) this nominal exchange rate will be determined according to the exchange rate regime and the monetary policy in place. In second place, we use a DSGE model in an economy with an infinite horizon, as is the OG. Thus, we are able to discuss the interesting equilibrium dynamics defining each exchange rate arrangement, as opposed to both D-D and C-V. In third place, we improve the way in which we introduce and treat potential crises, The potential for strategic complementarities and the realization of self-fulfilling prophesies is ever present in alternative versions of the OG model with outside assets in general, and models with one or more fiat currencies in particular6, and, of course, in our model. In such contexts, the presence of informational and institutional frictions can exacerbate situations that are already problematic, such as credit rationing, financial repression and endogenously arising volatility, thus complicating the standard analysis of separating and pooling equilibria. Thus, the appropriate utilization of the information and action sets available to agents at all points in time is critical. In this respect, we reformulate the sequential checking constraint by depositors and devise a re-optimization problem by banks after a sudden stop7.
Our results show the existence of a continuum of equilibria that are indeterminate in two ways: 1) an allocation may be consistent with a continuum of relative price vectors, and 2) a vector of relative prices may
3 See Kaminsky (2003) for details.
4 In their model, people held domestic currency because they derived utility from it, which in itself attached intrinsic value to the currency they intended to be fiat.
5 See Hernandez-Verme (2004) for the original discussion.
6 The recent literature on open economy macroeconomics has used intensively self-fulfilling prophecies as a tool that may lead to very important underlying explanations for financial fragility, currency crises and/or speculative attacks. See Cole and Kehoe (1996) and Obstfeld (1996).
7 In particular, one argument of the C-V framework was that when the probability of a crisis is public information, each agent in this economy must use this information when contemplating optimal plans of action at the beginning of every date, and, as result, the optimal behavior of agents is invariant with respect to whether the crisis was realized or not. Alternatively, we introduce the potential for uncertainty of the crisis by using a sunspot variable: a random variable unconnected to the fundamentals of the economy and that expresses the extrinsic uncertainty.
4
be consistent with several different allocations. There is a strong association between the scope for existence and indeterminacy of equilibria, the properties along dynamic paths and the underlying policy regime. Binding multiple reserve requirements may help in reducing the scope for financial fragility and panic equilibria, but backing of the domestic money supply has stabilizing effects only under fixed exchange rates.
The remainder of the paper proceeds as follows. In Sections 2 and 3, we analyze the properties of stationary and dynamic equilibria under the alternative exchange rate regimes where no crises are possible in equilibrium. In Section 4, we allow for the possibility of crises by introducing extrinsic and intrinsic uncertainties. Section 5 concludes.
2. Floating Exchange Rates: the Case of Indonesia, Korea, Philippines and Thailand
In this section, we build the model of a SOE that captures the main stylized characteristics shared by the Indonesian, Korean, Filipino and Thai economies at the time of the crisis. Here, we focus on the construction of the general equilibrium and, thus, we do not allow for any event that could lead to a crisis of any type. The reader interested can find the analysis of crises in Section 4.
The (private) banking sector is a net debtor with respect to the rest of the world, and there is an exogenous and binding upper limit to foreign credit faced by domestic banks at each point in time, so that credit is always rationed. We will observe ex-ante identical domestic agents who face uncertainty as to their preferences types. The distribution of this shock is public information, but its realization is known only by the private agents. Our model has the potential for strategic complementarities, taking the form of a standard problem in coordination that may lead to crises of a self-fulfilling type8. We will see that two fiat national currencies can potentially circulate simultaneously: a domestic fiat currency and a foreign fiat currency. The legal regulations in financial intermediation and foreign exchange establish the following: 1) All intermediated domestic investment is subject to multiple, unremunerated and binding reserve requirements. 2) A flexible exchange rate regime is in place, and thus the nominal exchange rate will be market-determined; and 3) There are no legal domestic restrictions on either using foreign currency or on obtaining foreign credit.
2.1 The Environment
Consider a pure exchange, SOE consisting of an infinite sequence of two-date-lived, overlapping generations.
Time is discrete, and indexed by t1, 2,3,.... Standard analysis of an overlapping-generations economy typically groups households into two categories: all the future generations versus the generation of initial old.
Moreover, we will observe four groups of players in this model economy: households, domestic banks, foreign
8 The decisions made by individual agents will be intertwined with the choices of other agents, giving rise to strategic interdependence between an agent’s actions and the actions of others.
5
banks and the domestic monetary authority. Foreign banks will lend to domestic banks inelastically at the world interest rates and up to the exogenous binding limit. The monetary authority in this model economy is in charge of choosing the combination of monetary policies consistent with floating exchange rates.
Each of the future generations, on the one hand, consists of a continuum of households with unit mass.
A household born at date t is young at date t and old at date t1. Households within a generation are ex ante identical, but they can become of one of the following types before the end of their youth: impatient, with probability (0,1), and patient, with probability (1). As we will see later on, impatient households will derive utility from consuming before the end of their youth (c1,t,) while patient households will derive utility only from consuming in their old age (c2, 1t .) On the other hand, at t0, there is a generation of initial old.
The initial old consist of a continuum of old households with unit mass. The fraction
1
of these initial old are of the patient type.Each date has two parts that we will call morning and afternoon, since different types of interaction will take place in each of them9. Domestic banks will turn out to be coalitions of individual households, they will be competitive, and we can assume then that they are identical. The latter facilitates the analysis by allowing the examination of only a representative bank.
Each date, there is a single endowment, tradable good. This good is homogeneous across households and countries, but it cannot be produced anywhere. When young, a domestic household receiveswunits of the single good, first thing in the morning. Old agents receive no endowments of any type.
The following equation represents the expected lifetime utility of an individual born at date t, with the information available at the beginning of this date.
1,, 2, 1
ln 1,
1
ln 2, 1t t t t t
E u c c c c . (1)
Households and domestic banks have access to the following storage/investment technology: for one unit of good invested –not consumed-- at the beginning of date t, the household receives the return R1 goods at the end of date t1. However, she would receive only a return of r1 if she were to liquidate the investment early, by the end of date t 10. Then, the condition to promote truth-telling can be written as
2, 1t 1,t
c r c . (2)
The inequality above must hold as the incentive-compatibility or self-selection condition that allows no motivation for patient agents to misrepresent their types. In the remainder of this section and in Section 3, we assume that the inequality (2) holds while we build the general equilibrium.
9 This separation is indispensable to our setup, because the sequence in which events take place and information becomes available are essential in determining the coordination between agents (or the lack of) and the nature of the information problem in place.
10The only available technology for the short-term investment is this same storage technology. For instance, if an agent liquidates early, she would get the return r 1 per good at the end of date t, and if she stores the proceeds again between the end of date t and the end of date t1, then she will get the return r r r2 1 R per good at the end of date t1. Thus, the long- term storage technology dominates early liquidation in rates of return.
6
Multiple Fiat Currencies. Two fiat and outside national currencies may circulate in the small, open economy at any point in time. The first one is the domestic fiat national currency, while the second is a foreign currency that serves also the purpose of international currency. To fix ideas, we will call the domestic currency the won11 and the foreign/international currency the US dollar 12.
On the first hand, it is apparent that the monetary authority in the domestic country has the monopoly in issuing wons, where Mt is the outstanding nominal stock of wons at the end of date t. The domestic price level pt represents the number of wons to be exchanged for one unit of the single good at date t, and
pt pt1
0 is the real return on wons. As is standard in economies with floating exchange rates, the monetary authority has the control over the nominal aggregate supply of wons, as we will see in detail in section 2.3. On the other hand, the US dollar may circulate in the domestic economy together with the won, and Qt represents the outstanding stock of foreign currency in the domestic country at the end of date t. The exogenous world price level pt* represents the number of US dollars that households need to exchange for one unit of the single good at date t, while
pt* p*t1
1*
1 0 represents the constant real return on US dollars, where * 1 is the exogenous net inflation rate in the rest of the world. It is apparent that Qt is endogenous, and it will depend on a group of variables such as foreign credit constraints binding, relative prices and policy rules, among others. Finally, we use et to denote the market-determined nominal exchange rate, measured as the number of wons exchanged for one US dollar.We also assume that there is free international capital mobility, free international trade with homogeneous goods and no legal restrictions to the use of foreign currency in the domestic country. As a result, the Law of One Price will hold in equilibrium, so that etp*t pt is always satisfied.
With respect to the general guidelines for monetary policy, the monetary authority in the domestic economy accomplishes all injections and/or withdrawals of wons through lump-sum transfers. In particular, each young household will receive the equivalent in wons of t goods ex ante, at the beginning of date t, regardless of type. We have two reasons behind our choice of this particular scheme of monetary transfers:
first, it enters the self-selection constraint neutrally without adding to the information problem, and second, it does not require the monetary authority to have additional information that could be of a private nature13.
At t0, the initial-old generation behaves as any old agent from the future generations would. In particular, a fraction
1
of these initial old individuals would be of the patient type, and, thus, would like to consume now. In standard models with overlapping generations, the initial conditions of the economy11 The won is the national currency of the Republic of Korea.
12 Obviously, in the case of the sub-prime mortgage crisis, the domestic currency would be the U.S. dollar.
13 We must point out that, in this framework, the question of ―who gets what and when‖ is not a trivial one, and different answers to it may have a crucial influence on the equilibrium results. The transfer scheme we propose may not be neutral, in the sense that it may affect the self-selection constraint, but it does affect both sides of it. In Appendix 1, we present results for the alternative case where the monetary authority gives transfers only to young agents who claim to be of the impatient type, after the realization of types.
7
describe the initial stock of the different assets that exist in the economy, and they play a key role. Typically, the initial stocks of outside assets indicate the ―endowments‖ of the members of the generation of initial old individuals .In the present case, there are two initial conditions: M0 0 and Q0 0 are given, and they are distributed equally among the patient initial old such that each has the equivalent of
M0e0Q0
/ 1
p0 goods early in date t0.2.2 Financial Intermediation
In our model, foreign banks play the somehow impersonal role of suppliers of international liquidity through foreign-credit instruments that may take different forms. Thus, the private banking sector in equilibrium is a net debtor of the rest of the world.
Domestic banks follow the standard D-D set up: a representative bank arises endogenously and pools together the resources owned by households with the purpose of providing them with partial insurance against the uncertainty of their potential types and with feasible allocations that are Pareto superior to autarky14. In the context of a small, open economy, domestic households may also benefit from pooling their resources and acting together whenever such economy does not display aggregate uncertainty, as is the case in our model economy.
Following the standard practice in the literature, a representative bank that starts business at date t will behave so that it maximizes the expected utility of the individual households born at date t, given by equation (1), which is also in the bank’s best interest as well. Henceforth, when we use the term ―banks‖
without further qualification, we refer to domestic banks starting business at t.
Access to Foreign Credit Markets. Only banks may access the world credit markets by trading with foreign banks in several primary debt markets, the idea being that the debt-instruments available may provide them with liquidity in a variety of terms and/or dates of maturity.
Banks have access to three different foreign-debt instruments. The amounts traded of the different instruments form the debt-structure vector denoted by
d0,t,d1, 1t,d2, 1t
, where all amounts are expressed in terms of the single good15. The vector of relevant prices associated with this debt-structure is denoted by
r r r0*, ,1* 2*
1. d0,t is a short-term intra-date loan issued early-morning in date t and maturing in late- afternoon of the same date, while d1, 1t stands for a short-term inter-date loan issued in the late afternoon of date t and maturing late in the afternoon of date t1. Finally, d2, 1t is a long-term loan issued early in the morning of date t and maturing late in the afternoon of date t1. We assume that each of the elements in the price vector
r r r0*, ,1* 2*
1 is a time-invariant and exogenous gross real interest rate determined in the14 See the section on deposit contracts for more details. Notice also that the intermediation equilibrium is not Pareto optimal since early liquidation is costly.
15 This treatment is standard in the literature. For the reader interested in the analysis of nominal debt denominated in different currencies, see Freeman and Tabellini (1998), Chang ( ) and Hernandez-Verme (2008.)
8
appropriate world financial market such that
d0,t,d1, 1t ,d2, 1t
0 and the vector
0, 0, 0
never obtains in equilibrium. Obviously, it follows that banks are net debtors of the rest of the world.Banks also face exogenous borrowing constraints on standing debt at each date, represented by
0,t 2, 1t 0
d d f , (3a)
1, 1t 2, 1t 1
d d f . (3b)
0 0
f and f1 0 are time-invariant and measured in terms of the single good. They are chosen exogenously by foreign banks, and represent the maximum foreign credit available at dates t and t1, respectively. (3a) and (3b) limit the total amount of foreign debt standing at each date, and we restrict our attention to allocations where (3a) and (3b) bind, so that foreign credit is rationed.
Fractional-Reserves Banking and Multiple Reserve Requirements. Multiple and unremunerated reserve requirements in our model follow Hernandez-Verme (2004.) All investment done by banks is subject to the financial regulations of the domestic country16. Out of the total deposits, a fraction must be held as currency reserves and only the remainder can be invested. A part of the currency reserves must be held in the form of wons, while the rest must be denominated in US dollars. In particular, the policy parameter d
0,1 denotes the fraction of total deposits that the banks must hold as currency reserves in the form of wons. When held between dates t and t1, domestic currency reserves earn the same return as real wons balances, namely
pt pt1
. Similarly, f
0,1 denotes the fraction of deposits that banks must hold in the form of foreign currency, with the return
pt* p*t1
. Obviously,
d
f 1 must hold, where
1d f
0 stands for the fraction of total deposits that banks can invest long-term. Finally, we must mention that we will focus on allocations where both reserves requirements are binding. This will transpire when
pt pt1
R and
p*t pt*1
R hold.Timing of Transactions17. In our model, there are no transactions among individual agents of any age or type, either domestically or with the rest of the world. All transactions take place through the banks. Thus, banks in this model are inherently financial intermediaries.
Individuals born at t live for four sub-dates: the morning and afternoon of date t, and the morning and afternoon of date t1. We now proceed to describe the transactions that take place each sub-date. Notice that only in this section we setup the budget constraints with the amount of early liquidation lt to facilitate a full understanding of the general bank’s problem, but in what follows we will return to the case where lt 0 The morning of date t:. Young individuals born first thing in the morning of date t have two sources of funds at this point: their endowment of w units of the single good, and the transfer of t goods from the monetary authority. Each of these young individuals deposits wt goods in a bank. On the other side of the
16 We further assume that all domestic investment is intermediated.
17 Timing of transaction in figure is available in Appendix.
9
financial market, we have banks receiving these deposits. Banks have also the ability to borrow from the rest of the world the amount of d0,t d2, 1t goods. They must also set aside the required currency reserves and bring them to their reserves account in the monetary authority. Banks combine these resources in order to finance the long-term investment kt that uses the domestic storage technology, leading to the budget constraint
0, 2, 1 (1 ) ( )
t t t f d t
k d d w . (4)
The afternoon of date t: Individual agents learn their types in the early afternoon of time t. Impatient agents will withdraw c1,t goods and consume them, while a patient agent would not withdraw, provided (2) holds.
Banks need to pay withdrawals in the amount of c1,t, and to repay r0*d0t of principal plus interest of intra-date foreign debt18. They also have a potential source of new funds at this point in the new short-tem foreign loan of d1, 1t goods. In case more funds were required, banks could liquidate early a part of the long- term investment (lt goods,) but they try to avoid doing so, since early liquidation is costly19. Summarizing, the budget constraint faced by a bank at the end of date t is
*
0 0, 1, 1
1,t d t r lt d t
c r
. (5)
The morning of date t1: There are no ―active‖ transactions in this sub-date. Both patient agents and banks wait for the duration of this sub-date. If all agents behave according to their true type, then all impatient agents have already consumed in the morning of date t.
The afternoon of date t1: At the end of date t1, agents of the patient type who behave according to their true type wish to withdraw funds to consume in their old-age (c2, 1t goods each.) Repayments of the long- term foreign debt
r2*d2,t1
and the new short-term foreign debt
r1*d1,t1
are due as well. A bank still in operation will use the return of the remaining long-term investment -given by R
kt lt
goods- together with the gross real return on its currency reserves to pay its obligations. It is helpful to notice at this point that one of the consequences of the regulations on reserve requirements concerning the financial sector in this economy is that banks have an additional source of funds at the end of t1 –even if they yield each a dominated real rate of return. This contributes to reduce the likelihood of a panic of patient depositors who did not want to withdraw at the end of date t. In brief, the budget constraint faced by a bank in late-afternoon of date t1 is given by
* *
2 1
2 1 2, 1 1, 1 *
1
1 ( )
1
f t t
t t t
t t t d
t
p w
c d d R k l w
r r p
. (6)
18 The parameter is public information, but all the banks know is that there are individuals of the impatient type and each shall withdraw c1,t goods. Banks do not know the identities of the truly impatient agents, and so they would allow total withdrawals amounting to c1,t goods to agents pretending to be of the impatient type, following a sequential service constraint of the form ―first come, first served.‖ In case the bank exhausts its resources before repaying all foreign loans that are due and all depositors left in the line for withdrawals, the bank closes, and any future payments contracted by the bank are lost.
19 In the sense that it obtains the effective return r 1 R instead. Moreover, we could think of short-term inter-date debt and early liquidations as substitute sources of liquidity for banks.
10
Deposit Contracts. Domestic individual agents face uncertainty about the type they will become at the end of their youth. Moreover, once realized, this information is private to each individual agent. Under these circumstances, the representative bank aims to protect itself by using some kind of self-selection mechanism.
Such a mechanism is designed to give individual agents the right incentives to behave according to their true type. In our particular case, this mechanism takes the form of the truth-telling constraint given by the inequality in (2). The severity of this private information problem in a particular state of the world will determine whether (2) will bind or not. For our convenience, henceforth, all of our analysis will refer to the general case of a generation born at date t, unless we explicitly say otherwise.
Autarkic Equilibrium. In the absence of financial intermediation, individuals cannot benefit from pooling their resources and there are no insurance schemes available to them. Thus, they could save only through their investment/storage technology. When the information about types is realized at the end of their youth, individual agents in autarky face a feasible set in the space of state-contingent commodities
c1,t,c2 1t
that contains only the point
r
wt
,R
wt
.Financial Intermediation. Recall that representative banks are coalitions of individuals in our model economy. These banks will offer to individuals a deposit contract consisting of the state-contingent pair
c1,t,c2, 1t
. Banks design this contract by choosing the pair c
1,t, c
2, 1t
that maximizes the individuals’lifetime utility described in (1), subject to the constraints (2)-(6). Interestingly, when financial intermediation is available to individuals, the feasible set consists of a continuum of state-contingent commodities. These deposit contracts may provide individuals with allocations that are Pareto-superior to that of autarky. In particular, notice that banks offer partial insurance against the uncertainty of types in the deposit contract, and they are capable of doing so due to their ability to pool the individuals’ resources. Individuals, in turn, are willing to sacrifice a little of potential returns in exchange for this insurance, so that
t
1,t 2, 1t
t
r w c c R w holds.
2.3 Conducting Monetary Policy under Floating Exchange Rates
In this model economy with flexible exchange rates, the monetary authority prioritizes two important aspects when conducting monetary policy: 1) the setting of the rate of domestic money growth, and 2) the choice of the appropriate backing of the domestic money supply with foreign-reserve assets20.
In the case of the first aspect, the growth rate of the domestic money supply becomes a tool of monetary policy of the utmost importance, as opposed to situations where the money supply is subordinated to other primarily chosen policy objectives. Many reasons may explain the special interest on this policy tool,
20 In this paper, we do not concern ourselves with the choice of the optimal rate of money growth or the optimal fraction of the money supply to be backed by the monetary authority. We do, however, provide some useful guidelines by discussing their effects on the existence and other properties of steady-state equilibria as well as the properties of the system along dynamic equilibrium paths.
11
other than the obvious --controlling the evolution of the domestic money supply--. First, it contributes to the control, up to some degree, over the determination of inflation rates, especially --but not only-- in the long-run.
Second, it is a mean of giving or taking away incentives to the actors involved with real activity –in our case, financial activity. Third, it can influence the formation of public expectations by keeping reasonable stable rates of inflation as well as the value of the national currency. We adopt the simplest scenario for our model economy, which contemplates the choice and setting, once-and-for-all, of a constant rate of money growth.
Such a policy sets the evolution of the supply of wons by the rule
1 1 , 0, 0 0
t t
M M t M , (7)
where 1 is the exogenous and constant rate of domestic money growth, chosen by the domestic monetary authority. The latter injects/withdraws money through lump-sum transfers to all young agents in the amount of
t goods each.
With respect to the second aspect, backing the domestic money supply is by itself a precautionary mechanism aimed to protecting this economy against potential reversals in the World financial market. This is also of key importance, given the significant amount of action this country has in foreign credit markets.
Typically, the monetary authority chooses and sets a fixed fraction of the money supply to be backed or guaranteed. Then, the backing takes the form of holdings of foreign, interest-bearing reserve assets in an amount equal to the dollar-value of this chosen fraction of the supply. This, of course, aims to stabilize the perceived value of money and the willingness of the public to hold it. Thus, the monetary authority holds Bt* dollars of foreign-reserve assets. These assets yield the interest rate r
1,R every date. These reserve- holdings evolve over time according to the rule* t
t
t
B M
e
, (8)where
0,1 is the exogenous and constant fraction of the dollar-value of the supply of wons backed by the monetary authority. This policy is a variation of the one used in Hernandez-Verme (2004)21.We now define zt
Mt pt
to be the per capita real balances of wons and bt* B
t*p
t*
to be the per capita holdings of foreign-reserve assets. When the two policy rules in (7) and (8) are adopted and combined by the monetary authority, its budget constraint at each date takes the following form:
* * * *
1 1 * *
1 * 1 1 1 1
t t t t
t t
t t t t t t
t t
B r B
M M
z b r b z r z
p p
p p
. (9)
Notice that equation (9) is a linear first order difference equation that describes the evolution of the real monetary transfer (t,) and that its dynamic behavior is inherited from zt.
21 Here, we assume for simplicity that there is no backing of domestic deposits. Notice that we use the symbol here to denote the coefficients in the first order difference equation that governs the long-term investment.
12
2.4 General Equilibrium under Floating Exchange Rates
Several sets of conditions must be satisfied simultaneously. We list them below.
First, there are two conditions on international transactions that apply to our small open economy.
One, since the single good is homogeneous across countries and there are no restrictions on the international trade of goods, it follows that purchasing power parity must hold, and, moreover, that the market-determined exchange rate et adjusts to ensure this condition is satisfied. Thus, we have
*
t t t
e p p . (10a)
Also, we confine our attention to vectors of prices
r r r0*, ,1* 2*
1 that satisfy the following no arbitrage condition, which controls for the different maturities of the three foreign-debt instruments:* * *
2 0 1
Rr r r . (10b)
Second, there are two constrains on the rates of return in this economy that imply that the reserve requirements are binding. This transpires when the following two conditions hold:
t t 1
R p p (11a)
*t *t 1
1 *
1R p p . (11b)
Third, we have all the conditions associated with the market for wons. One, the domestic price level pt clears the market for domestic real money balances:
t d t
z w . (12a)
The latter, in turn, leads to the equilibrium return of domestic real money balances
1
1 1 1
t t t t
p p z z (12b)
and, –using also (9) in the process, to the equilibrium laws of motion of zt and t, respectively
1 2 1
t t
z z , (12c)
1 2 1
t zt
, (12d)
where M 1 d 1d 1, 1 d w1 M ,
2 d r 1
M , 1 1 d w d and 2
2
d . Fourth, there is the market for foreign currency. This market clears when
t t t t f t f t d
q e Q p w z . (13a)
In equilibrium, qt and bt* are governed by the following two equations
1
2
1t f d f d t
q z , (13b)
*
1 2 1
t t
b z . (13c) Moreover, the endogenous growth rate of the supply of dollars in the domestic economy is given by
13
Qt1 Qt
1*
zt1
zt, (13d) while the nominal exchange rate follows:
et1 et
1
zt
1*
zt1
. (13e) Finally, there are several conditions that characterize deposit contracts in equilibrium. One, the truth- telling condition in (2) holds. Two, the constraints on foreign credit must bind, and thus0,t 2, 1t 0 and 1, 1t 2, 1t 1
d d f d d f . (14a)
Three, the representative bank’s long-term investment in equilibrium follows
1 2 1
t t
k z . (14b)
(14b) is a first order linear difference equation, and its reduced-form coefficients are given by
0
1 f 1 d f w
Ñ M and 2
1d f
r
1
M
, where 2 d 2d 1
Ñ . Next, the withdrawals offered by banks to impatient and patient individuals in equilibrium are, respectively
1 0
0*
0,1,t f f r 1 d t
c , (14c)
*
*
* * 2 2
2, 1 2 1 2, 1 1
1
1
1 1 1
1
1 1 1 1
f
t t t t
d
d t
t t
r r d r z z
w z
z z
c
Ж0
(14d)
where the intercept is given by
* 2 1 *
1 1
1 1 1 *
d w
r f
r
Ж0 . Notice that (14d) is a second
order, nonlinear difference equation in zt, and contemporaneous in d2, 1t . Last, we define the current account balance of this economy as22:
1 0*
0,
1 1*
1,
1 2*
2,
1, 1, 1
2, 2, 1
t t t t t t t t
CA r d r d r d d d d d . (14e) Notice that the first three terms on the right-hand-side of (14e) are negative. The reduced-form equations for the triplet
d0,t,d1, 1t ,d2, 1t
and, of course, the couple
c1,t,c2, 1t
will depend, as we will see in the next section, on the particular set of equilibria it belongs to.2.5 Multiplicity and Indeterminacy of Stationary Equilibria under Floating
In this section, we discuss the set of separating stationary equilibria. These equilibria are such that: 1) there are no misrepresentations of types; 2) there are no problems of liquidity, and 3) there is no early liquidation of the
22 We follow strictly the guidelines of the Manual of Balance of Payments by the IMF.
14
long-term investment by banks23. Before we proceed we must point the following: there is what we call a
“core” of variables that are independent of the foreign interest rates, and another set that contains foreign debt and state-contingent commodities that are determined as a result.
The Core in a Stationary Equilibrium. The core consists of a vector of five key variables:
zt, , ,t q b kt t*,
t
.These five variables are always determinate in equilibrium, since they do not depend on the interest rates
r r r0*, ,1* 2*
. Interestingly, the core dynamic system is de-coupled, inheriting its dynamics from zt. Notice that, under floating exchange rates,x ˆ
represents the steady-state value of the variable x. Thus, the stationary core can be found in the five equations that follow:
1 1 2 1
ˆ d w
z Э , (15a)
ˆ
1
1
1
ˆ z d w w d r d r
Э , (15b)
ˆ f ˆ d f 1
q z w Э , (15c)
b* zˆ
d w
1
Э ,
(15d)kˆ 1
2
zˆ, (15e)where Э
1d
1
r1
1 d
r1
. Notice that
z qˆ, ,ˆ b* are increasing in the policy parameters
, d,
and that, as expected, qˆ is increasing in f. In addition, ˆ is nonlinear in both andd but monotonically increasing in . Finally, kˆ is increasing in , but nonlinear in
d, f
. With respect to the steady-state returns on domestic and foreign real money balances, the growth of the nominal exchange rate and the growth rate of the real exchange rate, they are all constant and equal to
1
1,
1*
,
1
1 *
1 and 1, respectively.Foreign Debt in a Stationary Equilibrium. The amount that banks borrow from abroad is constant and non- negative in a stationary equilibrium, for all types of foreign debt-instrument, provided, of course that (10b) holds. Thus, the structure of foreign debt of a bank in a steady-state equilibrium is given by the triplet
d d d0, ,1 2
0. This stationary debt structure vector permits us to calculate the current account balance in a stationary equilibrium:
1 r0*
0
1 r1*
1
1 r2*
2 0CA
d
d
d
(16).We must remark that the deficit of the current account in stationary equilibria poses significant doubt on the long-run viability of this economy, as one might expect.
A stationary equilibrium then is defined as the allocation
zˆ, , , ,?qb
* kˆ, d d d
0,
1, 2l ˆ 0 5
3, which satisfies all the conditions given above. Of course, the
allocation of state-contingent commodities
c 1,c2 2 follows directly by using (14c) and (14d). The
23 In this section, we restrict our attention to equilibria where the conditions in the banks’ problem guarantee no early liquidation in equilibrium.
